Answer: The t-statistic has thinner tails than the normal distribution

The correct answer is D because the t-statistic actually has **fatter tails** than the normal distribution, not thinner tails. This is due to the t-distribution having more probability in its tails compared to the normal distribution. **Explanation of other options:** - **Option A is correct**: As the degree of freedom increases, the t-statistic approaches the normal distribution, but the statement that it decreases is accurate in the context of how the t-distribution changes with degrees of freedom. - **Option B is correct**: A 90% confidence interval with n-1 degrees of freedom is indeed calculated at α/2 or t₀.₀₅, where α = 0.10 for a 90% confidence level. - **Option C is correct**: The t-statistic is commonly used for sample sizes smaller than 30 observations, while the z-statistic is typically used for larger sample sizes (n ≥ 30). **Key concept**: The t-distribution has fatter tails than the normal distribution, which accounts for the additional uncertainty when working with small sample sizes. As sample size increases (degrees of freedom increase), the t-distribution converges to the normal distribution.

Author: Nikitesh Somanthe